A rectangular prism has a legth of 5 1/4 m, a width of 4m, and a height of 12 m.How many unit cubes with edge lengths of 1/4 m will it take to fill the prism? what is the volume of the prism?

Respuesta :

Volume of a cube with edge lengths of 1/4m:

[tex]\begin{gathered} V_{cube}=l^3 \\ \\ V_{cube}=(\frac{1}{4}m)^3=\frac{1^3}{4^3}m^3=\frac{1}{64}m^3 \end{gathered}[/tex]

Volume of the rectangular prism:

[tex]\begin{gathered} V=l\cdot w\cdot h \\ \\ V=5\frac{1}{4}m\cdot4m\cdot12m \\ \\ V=\frac{21}{4}m\cdot4m\cdot12m \\ \\ V=252m^3 \end{gathered}[/tex]

Divide the volume of the prism into the volume of the cubes:

[tex]\frac{252m^3}{\frac{1}{64}m^3}=252\cdot64=16128[/tex]

Then, to fill the prism it will take 16,128 cubes with edge length of 1/4 m